 
Summary: Towards a Quantum Monte Carlo approach
based on path resummations
Alexander James William Thom
Trinity Hall, Cambridge
Dissertation submitted for the degree of Doctor of Philosophy
at the University of Cambridge, December 2006
Abstract
This thesis is concerned with the development of a new reformulation of the Path
Integral method in terms of graphs rather than paths. In it we describe the re
formulation of the Path Integral method in a Slater determinant space. We have
developed a method of resumming paths in this space into graphs, objects on which
one can represent many paths. The signs of these graphs are very well behaved, with
a significant fraction being positive definite. The method in this form, however, is
unsuitable for large systems as it has a high scaling. To overcome this problem, we
recast the method in a form suitable for Monte Carlo evaluation; this process is not
possible for most correlated quantum chemical methods, which must instead resort
to significant levels of approximation.
We present some calculations on both the neon atom, and some small molecules
showing the ability of the full graph sums to describe molecular dissociation, even
in the very strongly correlated N2 molecule. We then demonstrate the accuracy of
